Imagine the Giants becoming a better team without Madison Bumgarner, suddenly soaring to new heights starting the day he was removed from the roster. It’s ridiculous to fathom, a fate that no one who has seen him pitch and hit would believe.

A story in Los Angeles is playing out that’s equally improbable — the Dodgers playing their most consistent ball in a truly unexpected streak that began when Clayton Kershaw got hurt.

It’s as if the Dodgers understood that Kershaw no longer could hold their hands, so they needed to walk across the street by themselves, and they realized they could look both ways and proceed on their own quite bravely and efficiently.

“Sometimes when the guy you lean on and helps you so much is gone, it makes everybody else pick up the slack,” Giants second baseman Joe Panik said. “Also, with the Dodgers, when you look at their lineup, it was kind of a matter of time before they turned the corner. They’ve got too many good hitters.”

When the Giants and Dodgers collide for a pivotal three-game series starting Tuesday at Dodger Stadium, Kershaw will be amping up his rehab, and he could pitch in minor-league games before the end of August. His back feels better, and the Dodgers are thinking the left-hander could appear late in the season for two or three starts. They’d make sure to align the rotation so that he could twice face the Giants, who play the Dodgers six times in their final 13 games.

Three left-handers, Clayton Kershaw, Scott Kazmir and Rich Hill, look to fortify the Dodgers’ rotation down the stretch. Kershaw and Hill have missed time this season with injuries.

Photo: Kevork Djansezian, Getty Images

The roster has come together in Kershaw’s absence, from an offense that leads the league in batting average and slugging percentage since the All-Star break to a worn and torn rotation that has done just well enough — even though manager Dave Roberts has used a whopping 13 starters — to a bullpen that has allowed the Dodgers to win the close ones.

“It’s been more a case of our struggles, too, with what’s happened since the break,” said Giants manager Bruce Bochy, referring to his team’s funk that coincided with the Dodgers’ surge. “They’re a very good club. They’re not based on one pitcher. They’ve got a balanced lineup and a lot of experienced pitchers who’ve filled in the holes.”

The Dodgers have made a run even though their biggest deadline deal, three pitching prospects to the A’s for Rich Hill and Josh Reddick, isn’t yet paying dividends. Perhaps it’ll start when the Giants come to town. Hill is due to make his Dodgers debut in Wednesday’s middle game, and Reddick is, well, due.

The right fielder has barely hit since leaving Oakland, 10-for-62 (.161) with just one extra-base hit and no RBIs. The Dodgers envisioned him as their cleanup hitter and a refreshing alternative to the troubled Yasiel Puig, who was unceremoniously demoted to Triple-A, but Reddick has been slow to adjust to the National League lifestyle.

Three weeks of watching Hill’s finger blister heal and Reddick’s numbers nosedive aren’t what the Dodgers anticipated when they sent three quality pitching prospects to the A’s, including Jharel Cotton, who threw 82/3 perfect innings for Triple-A Nashville before giving up a hit in a recent start. But they’re hoping Hill will pick up where he left off with the A’s (9-3, 2.25 ERA), and perhaps Reddick would rebound against a familiar foe.

Los Angeles Dodgers' Josh Reddick (11) in action during the ninth inning of a baseball game against the Philadelphia Phillies in Los Angeles, Wednesday, Aug. 10, 2016. The Philadelphia Phillies won 6-2. (AP Photo/Kelvin Kuo)

Photo: Kelvin Kuo, Associated Press

Then again, the Giants will start two left-handers, Bumgarner and newcomer Matt Moore, and Reddick has lousy numbers against lefties. In fact, Adrian Gonzalez, Corey Seager, Chase Utley and Joc Pederson all have significantly inferior numbers against lefties, which explains Moore’s presence and why the Giants tweaked their rotation so he’d pitch at Dodger Stadium.

The Dodgers are hitting .224 off lefties, worst in the majors. The Giants, with four everyday players hitting from the left side, rank 10th against lefties at .265.

When Kershaw last pitched, the Dodgers were 41-36 — 14-3 in Kershaw starts, 27-33 otherwise — and a season-high eight games behind the Giants. Since then, they’ve gone 26-19 and momentarily climbed atop the division until the Giants reclaimed first place Friday.

The Dodgers are considering starting Kenta Maeda, Hill and Brett Anderson against the Giants, who will counter with Bumgarner, Johnny Cueto and Moore.

Baseball with John Shea

Around the majors: Sad that Zack Wheeler had another setback in his rehab from Tommy John surgery. The ex-Giants farmhand probably will miss two full seasons and give it another crack with the Mets in 2017. The guy the Giants got for Wheeler, Carlos Beltran, still is going strong at 39, hitting above .300 for Texas. … The Twins are willing to part with former A’s catcher Kurt Suzuki, who cleared waivers. The Indians, Mets and Cardinals are teams in need of catching depth. … Teams have an advantage these days because live footage of most of their minor-league games can be seen through an app. So the Giants could get real-time information on Joe Nathan’s progress with Double-A Richmond. … Perfect placement of the Alexis Busch plaque, commemorating the Giants’ batgirl from the early 2000s who died in 2012. It could have been placed anywhere on the 12½-acre property, but it’s in the dugout right next to the bat rack in full view of Buster Posey, Hunter Pence and the boys each time they prepare to take their hacks. … For those suggesting the Giants’ chemistry took a hit without Matt Duffy, leading to their second-half slump, realize that once he got hurt, they went 13-7 to finish the first half with baseball’s best record. Still without him, they went 4-11 until the day he was traded to Tampa Bay. No pattern can be traced to his absence. … The other Matt Duffy, who played briefly for last year’s Astros, was picked up last month by the Rangers and is with Triple-A Round Rock. He faced Tim Lincecum in Lincecum’s debut at Salt Lake City, the Angels’ top affiliate, and homered in the 11th inning to win it.

John Shea is the San Francisco Chronicle's national baseball writer and columnist. He is in his 33rd year covering baseball, including 28 in the Bay Area. He wrote three baseball books, including Rickey Henderson's biography ("Confessions of a Thief") and "Magic by the Bay," an account of the 1989 World Series.